Загрузка данных

    gmp <- read.table("https://raw.githubusercontent.com/SergeyMirvoda/da2016/master/classwork4/gmp.dat")
    gmp$pop <- gmp$gmp/gmp$pcgmp
estimate.scaling.exponent <- function(a, y0=6611, response=gmp$pcgmp,
                                        predictor = gmp$pop, maximum.iterations=100, deriv.step = 1/100,
                                        step.scale = 1e-12, stopping.deriv = 1/100) {
  mse <- function(a) { mean((response - y0*predictor^a)^2) }
  for (iteration in 1:maximum.iterations) {
    deriv <- (mse(a+deriv.step) - mse(a))/deriv.step
    a <- a - step.scale*deriv
    if (abs(deriv) <= stopping.deriv) { break() }
  }
  fit <- list(a=a,iterations=iteration,
              converged=(iteration < maximum.iterations))
  return(fit)
}
   estimate.scaling.exponent(0.15)
## $a
## [1] 0.1211533
## 
## $iterations
## [1] 58
## 
## $converged
## [1] TRUE

Функция удаления строки

plot.with.dif.point.and.a <- function(a = 0.15,clear.row = 0){
  
  if(clear.row==1){
    row.for.clear <- sample.int(nrow(gmp),1)
    Select <-  which(!(1:nrow(gmp)) %in% row.for.clear)
    gmp <<-gmp[Select,]
  }
  gmp$predicted <- 6611*(gmp$pop)^estimate.scaling.exponent(a)[[1]]
  p.plot <- plot(pcgmp~pop, data=gmp, xlab="Население", log="xy",ylab="Доход на душу населения ($/человеко-год)", main="Метрополии США, 2006")
  print(paste("a:",estimate.scaling.exponent(a)[[1]],"iterations:", estimate.scaling.exponent(a)[[2]]))
  print(p.plot)
  print(lines(gmp$pop, gmp$predicted, col = "red"))
}

Вызов функции с разным а и вызов функции с удалением случайных точек

      plot.with.dif.point.and.a(0.3)

## [1] "a: -2.85063412085793 iterations: 2"
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      plot.with.dif.point.and.a(0.25)

## [1] "a: -0.475270609311027 iterations: 100"
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      plot.with.dif.point.and.a(0.2)

## [1] "a: 0.121153292739596 iterations: 70"
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      plot.with.dif.point.and.a(0.15)

## [1] "a: 0.121153292739624 iterations: 58"
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      plot.with.dif.point.and.a(0.1)

## [1] "a: 0.121153292739592 iterations: 61"
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      plot.with.dif.point.and.a(0.05)

## [1] "a: 0.121153292739596 iterations: 69"
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      plot.with.dif.point.and.a(0.12)

## [1] "a: 0.121153292739596 iterations: 54"
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      for(i in 1:365){
        plot.with.dif.point.and.a(0.12,1)
      }

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Были построены графики, которые показывают постепенное удаление точек:

  1. Было установлено, что показатель “а” меняется незначительно и держится около 0.12 и количество итераций держится в одном интервале, нестабильное значение итераций проявляется при удалении значимых точек
  2. Чем ближе стартовое значение “а” к искомой “а”, тем меньше количество итераций ***